Effective Borehole Thermal Resistance Research Articles

Generic modelling to develop thermal yield nomograms for coaxial deep borehole heat exchangers (DBHEs)

Numerical modelling of coaxial deep borehole heat exchangers (DBHEs) can be resource-intensive. Simpler, transparent analytical models and nomograms would be valuable to developers and geologists for evaluating thermal output. In this paper, Beier’s published analytical computational model was used to produce nomograms of geothermal heat yield by systematically varying the DBHE depth and rock thermal conductivity, while assuming two generic simplified DBHE designs, a geothermal gradient of 25°C km −1 and a fluid circulation rate of 5 l s −1 . Continuous 25 year heat yields from a 1000 m DBHE range from 27.3 to 54.8 kW for thermal conductivities of 1.6–3.6 W m −1 K −1 . For a 3000 m DBHE, they range from 165 to 281 kW. Effective borehole thermal resistance ( R b,eff ) increases strongly as DBHE depth increases due to internal heat transfer between the upflow and downflow elements. Simulations correspond well with results from industry-standard Earth Energy Designer software for a shallow 200 m coaxial BHE. They modestly underestimate the OpenGeoSys numerical modelled thermal yields by 2–4% for DBHE in the depth range 1000–3000 m. Modelled temperature evolution closely approximates an analytical ‘line heat source’ approach, implying that simpler analytical approaches are plausible for DBHE simulation. Future research should focus on methods for forward quantification of R b,eff .

Comparative analysis of ground thermal conductivity and thermal resistance of borehole heat exchanger in different geological layered sequence

Borehole heat exchanger usually passes through many geological layers of the different thermo-physical properties from one layer to another in practical project of ground-coupled heat pump system. Considering the effect of heterogeneity in geological structures on heat transfer of borehole heat exchanger, it is necessary for in-situ thermal response test analysis to investigate the effect of geological layered sequence on ground thermal conductivity and borehole thermal resistance. Firstly, based on the validated numerical layered borehole heat exchanger model and numerical homogenous borehole heat exchanger model, the simulated distributions of water temperatures in U-pipe and heat flux along the depth in thermal response test are respectively compared and analysed. Then, the effective thermal conductivity and effective borehole thermal resistance estimated by the infinite line source model are respectively obtained based on the simulated thermal response tests carried out in the borehole heat exchanger installed in the six types of geological layered structures. The borehole thermal resistances in the two numerical model were respectively calculated by integrating the local thermal resistance along the depth. Finally, the ground thermal conductivities and borehole thermal resistances are compared in six types of geological layered structures. The results show that the maximum relative error of 7 % between the effective thermal conductivity and the thickness-weighted thermal conductivity in the numerical layered borehole heat exchanger model is located in the sequence of S-L-C due to BOTTOM 60m-thickness clay with lowest thermal conductivity. The relative error between effective borehole thermal resistance and borehole thermal resistance in the numerical layered borehole heat exchanger model are 3.5 %∼7.9 % in the six types of layered geological structures, and the maximum relative error between the two borehole thermal resistances corresponding to the two numerical models is only 1.1 %, which proves that effect of geological layered sequence on the deviation is limited in the two numerical models.

Effect of seepage condition in geological stratification on thermal response test analysis of borehole heat exchanger

Determination of ground thermal properties is the prerequisites for the design of ground-coupled heat pump systems (GCHPs), and it is crucial for evaluating the thermal performance of borehole heat exchangers (BHEs). These parameters are usually obtained by in-situ thermal response test (TRT) based on infinite line source model (ILSM). Though the effect of the groundwater flow on the estimation of ground thermal parameters is considered in homogenous ILSM, the estimated deviation can be enlarged as seepage condition varies based on the BHE model in practical geological stratification. Based on the developed numerical layered seepage BHE model (NLSBM), this paper evaluates the effects of seepage location and seepage velocity on estimated accuracy of borehole thermal resistance and ground thermal conductivity. Relative error (RE) between effective thermal conductivity λeff and the thickness-weighted thermal conductivity λTW will be up to 30.5% with the increase of the thickness of the seepage layer. The relative error between λeff and λTW increases from 5.3% to 93.5% when seepage velocity changes from 1 × 10−6 m/s to 1 × 10−4 m/s. The minimum RE between borehole thermal resistance Rb,NLSBM and effective borehole thermal resistance Rb,eff is still up to 37% when seepage locates in the 5th layer. With the increase of the seepage velocity, the RE between Rb,eff and Rb,NLSBM is enlarged, and the minimum RE is up to 29.4% corresponding to the lowest seepage velocity of 1 × 10−4 m/s. The change of seepage velocity or seepage location has little effect on Rb,NLSBM, and the highest RE is only 0.2%.

Uncertainty quantification of borehole heat exchanger design length based on a global sensitivity analysis

Ground heat exchangers are essential components of ground-source heat pump systems. One of the most-used ground heat exchanger types is a borehole heat exchanger (BHE). Many parameters, such as the building thermal loads, ground thermal properties, and BHE components, influence the required BHE length. Therefore, understanding how individual parameter uncertainties are propagated to the output is counterintuitive. In this study, a global sensitivity analysis (GSA) was performed using the framework of the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) BHE design method. The GSA was conducted to identify the subparameters behind the input parameters of ASHRAE design method, which indirectly determine the BHE lengths by impacting the direct input parameters in the ASHRAE formula. The results reveal that the zone infiltration, heat pump efficiency, ground temperature, effective borehole thermal resistance, and electric equipment heat gain are the most influential parameters on the BHE design length.

Effective Thermal Conductivity and Borehole Thermal Resistance in Selected Borehole Heat Exchangers for the Same Geology

Investigating the constructions of borehole heat exchangers with high efficiency (unit heat transfer between the heat carrier and ground) is important. One of the means to improve efficiency is the use of the most efficient construction of the borehole heat exchanger. The paper describes research on borehole heat exchangers’ thermal efficiency, which is mainly characterized by parameters obtained from a thermal response test: effective thermal conductivity and borehole thermal resistivity. The borehole heat exchangers of the Laboratory of Geoenergetics in Poland were studied. Based on thermal response test interpretation and empirical equations, one of which is proprietary, the heat transfer is calculated independent of the duration of the thermal response test. Other conditions for using borehole heat exchangers in downtowns are discussed. The research aims to determine the best borehole heat exchanger design from five basic possibilities studied. A lack of unequivocal statements regarding this matter in the literature was observed. The influence of the interpretation method on the research results is determined. A single U-tube system filled with gravel is shown to be the most advantageous design by a very small margin. The applied interpretation methods, however, confirm the hitherto ambiguity in the selection of the best construction. The maximum heat carrier temperature at the end of thermal response tests was 32 °C for a geological profile mostly made up of clay (low thermal conductivity) and 23 °C for Carpathian flysch (sandstones and shales, with a higher value of conductivity).

Study on the best heat transfer rate in thermal response test experiments with coaxial and U-pipe borehole heat exchangers

This paper concerns the modeling of vertical Borehole Heat Exchangers (BHEs) for Ground Source Heat Pump (GSHP) applications. Focus is devoted to the analyses of Thermal Response Test (TRT) simulations aimed at understanding the main factors that influence the ground thermal conductivity and the effective borehole thermal resistance estimations. The conventional infinite line-source (ILS) model does not include any influence of the external heat transfer rate on the BHE/ground property evaluation. Analyses of numerically simulated TRTs show this omission can sometimes produce an error in the estimate of the ground thermal conductivity. The error may be between ±10% and ±22% for coaxial boreholes (800 m depth), if the ground has a significant geothermal gradient. On the other hand, for single and double U-pipe BHEs the error is less than ±5% under similar conditions. The parameter qratio is identified as an indicator of when the error is significant. This parameter is equal to the external heat rate (injection or extraction) divided by a natural heat rate that is related to the geothermal gradient. Errors greater than ±10% tend to occur for coaxial boreholes with a center-pipe fluid inlet when |qratio| < 1. Under the same conditions but with the annulus as the fluid inlet, the error is less than ±6%.

The coupled two-step parameter estimation procedure for borehole thermal resistance in thermal response test

The ground thermal properties and borehole thermal resistance are the essential parameters for the design of borehole heat exchanger (BHE) field, and they are usually estimated using the experimental inlet/outlet fluid temperatures of BHE in thermal response test (TRT). This paper proposes the coupled two-step parameter estimation procedure (TSPEP) for estimating ground thermal conductivity and borehole thermal resistance of BHE by evaluating the actual averaged–over-the –depth mean fluid temperature (MFT) using the quasi-three-dimensional model inside the borehole. The simulated annealing algorithm (SAA) is used to iteratively find the minimum values of the two objective functions to obtain the optimal estimated results. In TSPEP, the estimated ground volumetric heat capacity and weighted factor f in the 1st step are transferred to calculate MFT using the experimental data in the 2nd step, which guarantees the direct approach based on the infinite line source model (ILSM)applied to improve the accuracy of the estimated borehole thermal resistance. For 50 m depth BHE, the estimated borehole thermal resistance is increased by 12.1% using TSPEP than the effective borehole thermal resistance evaluated by the arithmetic average fluid temperature (AFT). The estimated ground thermal conductivity in TSPEP is almost same with that from the direct approach based on ILSM, and the maximum relative error between them is only 0.91% even though borehole depth of BHE changes from 50 m to 200 m.

Relation Between Mean Fluid Temperature and Outlet Temperature for Single U-Tube Boreholes

Ground-coupled heat pump (GCHP) systems usually utilize buried vertical heat exchangers, named borehole heat exchangers (BHEs). The accurate design or simulation of a GCHP system requires the calculation of the time-dependent outlet temperature from the BHEs, Tout. However, the most widely employed BHE simulation models yield the time evolution either of the mean temperature of the BHE-ground surface, Tsm, or of that of the fluid, Tfm. In transient regime, it is not easy to relate Tout to either Tsm or Tfm. In this paper we determine, through 3D finite element simulations, simple expressions of a dimensionless coefficient φ allowing the calculation of Tout by means of a simulation model that yields Tfm. These expressions hold for single U-tube BHEs, both in quasi-steady and in unsteady working conditions. We validate our 3D simulation code by comparison with an analytical BHE model. Then, we present applications of our expressions of φ to calculate the time-dependent values of Tout through a BHE model that yields those of Tfm. Finally, we show that the values of φ in quasi-steady working conditions can be used for a simple calculation of the effective borehole thermal resistance.

Effect of depth and fluid flow rate on estimate for borehole thermal resistance of single U-pipe borehole heat exchanger

Accurate estimates for ground thermal parameters and borehole thermal resistance are important to improve the design of borehole heat exchangers (BHEs) in ground-coupled heat pump systems(GCHPs). In order to improve the estimating accuracy of borehole thermal resistance, this paper presents a simple analytical method for evaluating the actual averaged –over-the –depth mean fluid temperature (MFT) in the U-pipe of BHE to calculate borehole thermal resistance Rb. Furthermore, the effects of borehole depth and volumetric flow rate on the calculating RMSE distribution between borehole thermal resistance Rb and effective borehole thermal resistance Rb∗ are investigated. The conclusion shows that the relative deviation between the two borehole thermal resistances corresponding to the volumetric flow rate 1.5e-4m3/s increases from 4.2% to 29.7% when borehole depth changes from 50 m to 200 m. Finally, the borehole depths corresponding to different volumetric flow rate are optimized to find the boundary line where Rb are nearly equal to Rb∗ in the operating time, and the impacts of grout thermal conductivity and heat rate per unit depth of BHE on the boundary line are quantitatively analyzed. Volumetric flow rate has more effect on Rb with the higher grout thermal conductivity, the relative error between the two Rb corresponding to V = 1.5e-4m3/s and V = 3e-4 m3/s is 10.8% for kg = 2.3 W/(m.°C). The effect of heat rate per unit depth of BHE on Rb is very limited, the relative error between the two Rb corresponding to q1=50 W/m and q1=80 W/m is 5.4% under V = 1.5e-4m3/s, and it is only 3.7% under V = 3e-4 m3/s.

Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers

Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.

Design optimization of the borehole system for a plus-Energy kindergarten in Oslo, Norway

ABSTRACTThis paper presents the case study of a newly constructed 1600 m2 kindergarten building in Oslo, Norway. The building has been designed within the framework of the Norwegian Research Council Project LowEx, which aims at engineering solutions to achieve a seasonal coefficient of performance (SCOP) of 6–10 for heating, a seasonal energy efficiency ratio (SEER) of 80–100 for cooling, and an 80% reduction in the purchased electric energy for heating and cooling of the buildings. Several architectural and technical measures have been implemented in the case study building to meet these requirements. This paper first provides an account of the design measures implemented in the building to achieve the ambitious energy performance targets. It then focuses on the design of the ground source heating and cooling system for the building and presents the preliminary design of the borehole system to provide low-temperature heating and high-temperature cooling to the kindergarten. The possibility of improving the borehole system design by optimizing the solar heat gains through the building envelope to balance the ground thermal loads is explored next. Finally, the effect of uncertainties in the design input values of ground thermal conductivity, effective borehole thermal resistance, and undisturbed ground temperature on the final design of the borehole system is evaluated.

Evaluation of the Internal and Borehole Resistances during Thermal Response Tests and Impact on Ground Heat Exchanger Design

The main parameters evaluated with a conventional thermal response test (TRT) are the subsurface thermal conductivity surrounding the borehole and the effective borehole thermal resistance, when averaging the inlet and outlet temperature of a ground heat exchanger with the arithmetic mean. This effective resistance depends on two resistances: the 2D borehole resistance (Rb) and the 2D internal resistance (Ra) which is associated to the short-circuit effect between pipes in the borehole. This paper presents a field method to evaluate these two components separately. Two approaches are proposed. In the first case, the temperature at the bottom of the borehole is measured at the same time as the inlet and outlet temperatures as done in a conventional TRT. In the second case, different flow rates are used during the experiment to infer the internal resistance. Both approaches assumed a predefined temperature profile inside the borehole. The methods were applied to real experimental tests and compared with numerical simulations. Interesting results were found by comparison with theoretical resistances calculated with the multipole method. The motivation for this work is evidenced by analyzing the impact of the internal resistance on a typical geothermal system design. It is shown to be important to know both resistance components to predict the variation of the effective resistance when the flow rate and the height of the boreholes are changed during the design process.

Validation of borehole heat exchanger models against multi-flow rate thermal response tests

A recently developed vertical borehole ground heat exchanger model that accounts for transit time effects and time-varying short-circuiting heat transfer has been validated against two multi-flow-rate thermal response tests (MFR-TRT). The MFR-TRT, when performed with a wide range of flow rates, results in significant changes in the borehole thermal resistance, the borehole internal thermal resistance, and the short-circuiting heat transfer between the two legs of a single U-tube. The model accounts for short-circuiting by an analytically computed weighting factor that is used to determine the mean fluid temperature. The weighting factor portion of the model can be readily utilized in other ground heat exchanger models that currently rely on a simple mean fluid temperature. Use of the weighting factor is shown to give significantly better estimations of entering and exiting fluid temperature than using the simple mean fluid temperature. The new model is also compared to an alternative approach − using an effective borehole thermal resistance. While both the effective borehole thermal resistance model and the weighting factor give quite good results a few hours after a step change in flow rate, the weighting factor model gives much better results in the first few hours after a step change in flow rate.

An Experimental Study on the Thermal Performance Evaluation of SCW Ground Heat Exchanger

In recent years, application of the standing column well (SCW) ground heat exchanger (GHX) has been noticeably increased as a heat transfer mechanism of ground source heat pump (GSHP) systems with its high heat capacity and efficiency. Determination of the ground thermal properties is an important task for sizing and estimating cost of the GHX. In this study, an in situ thermal response test (TRT) is applied to the thermal performance evaluation of SCW. Two SCWs with different design configurations are installed in sequence to evaluate their effects on the thermal performance of SCW using a single borehole. A line source method is used to derive the effective thermal conductivity and borehole thermal resistance. Effects of operating parameters are also investigated including bleed, heat injection rate, flow rate and filler height. Results show that the effective thermal conductivity of top drawn SCW (Type A) is 11.7% higher than that of bottom drawn SCW (Type B) and of operating parameters tested bleed is the most significant one for the improvement of the thermal performance (40.4% enhanced in thermal conductivity with 10.9% bleed).

Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

The borehole thermal resistance – that is, the thermal resistance between the fluid in the U-tube and the borehole wall – is both a key performance characteristic of a closed-loop borehole ground heat exchanger and an important design parameter. Lower borehole thermal resistance leads to better system performance and/or lower total borehole length and possibly lower installation costs. Borehole thermal resistance may be determined using in situ thermal response testing, but for design purposes, it is important to be able to predict the borehole thermal resistance prior to installation. Due to the complexity of calculating it, numerous simplified methods have been proposed. This paper reviews published methods for calculating borehole thermal resistance for grouted boreholes with single U-tubes and compares their results against a rigorous analytical method.Another quantity that is particularly important for deep boreholes is the internal thermal resistance – that is, the thermal resistance between the upward-flowing and downward-flowing fluid paths in the borehole. Short-circuiting between the two legs has the effect of reducing the total heat transfer and can be quantified as an adjustment to the borehole thermal resistance, resulting in an effective borehole thermal resistance. A few simplified methods for calculating internal thermal resistance are compared against a rigorous analytical method.The simplified methods for calculating both borehole thermal resistance and internal thermal resistance are compared in parametric studies spanning the range of borehole diameters, pipe spacing, ground thermal conductivities and grout thermal conductivities found in practice. Many of the simplified methods work well with some combinations of parameters and poorly with others. The first-order multipole expressions are closed-form algebraic expressions that give results within 2% (for borehole thermal resistance) and 6% (for internal thermal resistance) over the entire range of parameters. This represents significantly better accuracy than any of the other simplified methods and, therefore, the first-order multipole algorithm is recommended for single U-tube applications when the tubes are symmetrically placed.

Design of spiral coil PHC energy pile considering effective borehole thermal resistance and groundwater advection effects

This study presents experimental and numerical research results in determining an effective borehole thermal resistance of a spiral coil energy pile. A precast high-strength concrete (PHC) energy pile with a spiral coil GHE was installed and thermal response test was carried out to evaluate the thermal behavior of the energy pile and to validate the effective borehole thermal resistance. Besides, parametric studies using a numerical analysis were carried out to suggest a multiple regression equation for the effective borehole thermal resistance of spiral coil energy piles. The adjusted coefficient of determination (adjR2) of the regression equation was 92.4%, which was also verified by comparison with experimental results. Furthermore, using current analytical models, this paper examined the effect of groundwater advection on the long-term ground temperatures. In the long-term period operation, groundwater advection attenuates the average temperature rise in the ground compared to the case with the absence of groundwater advection, and this phenomenon ultimately causes a decrease of the temperature penalty value. The temperature penalty value, considering the effect of groundwater advection, was calculated and compared for various groundwater advection velocity values in different pile arrays.

Effective Borehole Thermal Resistance of A Single U-Tube Ground Heat Exchanger

The effective borehole thermal resistance of a vertical, single U-tube ground heat exchanger is numerically studied. The nonuniform temperature distributions along the perimeter of both borehole and outside diameter of two pipes are taken into account to evaluate effective borehole thermal resistance. A best-fit correlation for effective borehole thermal resistance is proposed, and the dimensionless borehole thermal resistances are compared between the present correlation and other available equations in the literature. It is found that the present correlation of effective borehole thermal resistance is more accurate than those of available formulas.

Finite line-source model for borehole heat exchangers: effect of vertical temperature variations

A solution to the three-dimensional finite line-source (FLS) model for borehole heat exchangers (BHEs) that takes into account the prevailing geothermal gradient and allows arbitrary ground surface temperature changes is presented. Analytical expressions for the average ground temperature are derived by integrating the exact solution over the line-source depth. A self-consistent procedure to evaluate the in situ thermal response test (TRT) data is outlined. The effective thermal conductivity and the effective borehole thermal resistance can be determined by fitting the TRT data to the time-series expansion obtained for the average temperature.

First in situ determination of the thermal performance of a U-pipe borehole heat exchanger, in Cyprus

A ground heat exchanger can be used for the injection or extraction of thermal energy into/from the ground. The line source model is an easy method of evaluating the characteristics of the borehole and does not need expensive equipment. This method is presented and a test is performed in order to determine a borehole’s characteristics in layers consisting of clay, silt and sand at various analogies. For the borehole under test the ground thermal conductivity ( λ) was found to be 1.605 W/(m K) and the effective borehole thermal resistance ( R b) to be 0.257 K/(W/m). The accuracy of the collected data could be affected mainly by two factors. The first factor is the daily flux penetration through the ground which gradually increases the temperature of the top layers and the second factor is a variation of the heating coil injection rate per active length of borehole. As it was observed this combined effect has a negligible result on the mean fluid temperature during the test hours of 280–400, when the system was operating at steady state. The steady state conditions yield values of borehole thermal resistance which deviates about 25% from the values given by the line source method. The ground thermal conductivity deviates only about 5%. This method however is not suitable for estimating the above values because of the uncertainty that exists in the estimation of the mean ground temperature, which is not constant throughout the borehole length nor is it constant at different points in a cross section of the grout. Also this method takes a lot of time until the steady state is reached.